Antennas made of lengths of wire are frequency sensitive as the length of wire approaches even intervals of operating wavelength, .lambda., i.e., .lambda./4, .lambda./2, .lambda., 2.lambda., 4.lambda., etc. An antenna of infinite length and configured according to a standard Archimedian or logarithmic geometry theoretically would operate independently of frequency of operation since its critical dimension would be defined by angle only. This being both impossible and impractical, there are two basic approaches to the design of "frequency-independent" (FI) antennas: 1) "shaping" of the wire layout of the antenna to specify antenna operation entirely by angles, and 2) "complementary shaping" such that the critical dimension of the wire itself, usually the longitudinal dimension, repeats in terms of .lambda.. Examples of the first type are planar and conical equiangular spiral antennas, while those of the second type include log-periodic antennas. Further, by combining the best features of both approaches, i.e., periodicity and angle concepts, antennas having high bandwidths can be made. The designer is free to combine elements but when limited by packaging constraints such as those for aerospace vehicles, the antenna designer must seek alternative solutions when a requirement exists to extend the operating bandwidth to low operating frequencies, i.e., a physically long .lambda..
For an equiangular spiral antenna, energy radiates as the wave progresses along the antenna. Beyond that distance correlating to the circumference of the spiral that equals the operating .lambda., the antenna can be terminated. This determines the lowest frequency of operation. Hence, for a low frequency of operation, c/.lambda., a large circumference will be required, resulting in a large package to confine the antenna.
The precision at the input to the spiral determines the highest frequency of operation for the spiral antenna. Given that the mathematical representation for the radius to be used at an operating frequency corresponding to .lambda..sub.1 is: ##EQU1##
where:
r.sub.1 =radial distance to the spiral corresponding to operating .lambda..sub.1, cm PA1 r.sub.0 =fixed radius of the spiral antenna, cm PA1 a=constant related to rate of expansion of the antenna PA1 .phi..sub.1 =angle at r.sub.1, radians PA1 .phi..sub.0 =angle at r.sub.0, radians PA1 .lambda..sub.1 =operating .lambda. for a frequency-independent design at r.sub.1, cm PA1 .lambda..sub.2 =operating .lambda. for a frequency-independent design at r.sub.2, cm PA1 r.sub.2 =radial distance to the spiral relating to operating at .lambda..sub.2, cm PA1 .phi..sub.2 =angle at r.sub.2, radians PA1 D=outer diameter of the spiral, cm PA1 N=required highest order mode of operation PA1 .lambda.=wavelength of basic frequency of operation, cm PA1 bandwidth extension to lower frequencies while incurring little or no penalty in package size; PA1 use of existing packages for systems able to operate at bandwidths extended to lower frequencies; PA1 reduction in antenna arm length of approximately 25% per octave bandwidth; PA1 flexibility in adjusting design parameters of bandwidth and polarization quality; PA1 simplified design of alternate configurations; PA1 inexpensive fabrication; PA1 low maintenance; PA1 high reliability since there are no additional components or moving parts; and PA1 ready upgradability of existing systems.
then, when operation changes to a new frequency corresponding to .lambda..sub.2, the radial distance, r.sub.2, for an FI spiral antenna will be given by: ##EQU2##
where:
and, thus: ##EQU3##
where:
The frequency coverage of a spiral antenna is inversely related to the inner and outer radii of the spiral itself. The inner radius determines the high frequency limit of operation and the outer radius the lower. The relationship describing the low frequency limit is given by: ##EQU4##
where:
Attendant requirements for lower operating frequencies for new receiver and direction finding (DF) equipment have driven a number of attempts to broaden bandwidth response in a small package, all with very limited success usually resulting in overall performance degradation. Previous efforts at extending bandwidth to lower operating frequencies, so as to electrically lengthen the antenna without a proportional physical lengthening, included: 1) dielectric loading above or below the plane of the antenna such as described in U.S. Pat. No. 3,624,658, issued to Voronoff; 2) various resistive terminators for the antenna's arms such as described in U.S. Pat. No. 3,828,351, issued to Voronoff; and 3) symmetrically modulated arms such as described in U.S. Pat. No. 4,605,934, issued to Andrews. The most significant improvements evolved from a combination of planar and helical spiral arms, at the expense of a much larger package, such as described in U.S. Pat. No. 4,658,262, issued to DuHamel.
A requirement for an FI antenna both 1) able to operate within a bandwidth having an extended low operating frequency, i.e., at a longer .lambda., and 2) able to fit in existing packaging, created an as yet unmet need. Given the immutable nature of the conventionally-designed spiral or helical antenna in all of its mutations as described above, this need has not yet been filled. However, the need is addressed by a preferred embodiment of the present invention.